A criterion for weak mixing of induced interval exchange transformations

Let $f\text{\hspace{0.17em}⁣}:X\to X$, $X=[0,1)$, be an ergodic IET (interval exchange transformation) relative to the Lebesgue measure on $X$. Denote by $f_t\colon X_t\to X_t$theIETobtainedbyinducing$f$tothesubinterval$X=[0,t)$,$0<t<1$. We show that $$\{0<t<1\mid f_t\text{is weakly mixing}\}$$ is a residual subset of $X$ of full Lebesgue measure. The result is proved by establishing a generic Diophantine sufficient condition on $t$ for $f_t$ to be weakly mixing.